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This article is cited in 2 scientific papers (total in 2 papers)
On Lagrangians with Reduced-Order Euler–Lagrange Equations
David Saunders Department of Mathematics, Faculty of Science, The University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
Abstract:
If a Lagrangian defining a variational problem has order $k$ then its Euler–Lagrange equations generically have order $2k$. This paper considers the case where the Euler–Lagrange equations have order strictly less than $2k$, and shows that in such a case the Lagrangian must be a polynomial in the highest-order derivative variables, with a specific upper bound on the degree of the polynomial. The paper also provides an explicit formulation, derived from a geometrical construction, of a family of such $k$-th order Lagrangians, and it is conjectured that all such Lagrangians arise in this way.
Keywords:
Euler–Lagrange equations; reduced-order; projectable.
Received: January 26, 2018; in final form August 23, 2018; Published online August 25, 2018
Citation:
David Saunders, “On Lagrangians with Reduced-Order Euler–Lagrange Equations”, SIGMA, 14 (2018), 089, 13 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1388 https://www.mathnet.ru/eng/sigma/v14/p89
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Abstract page: | 139 | Full-text PDF : | 24 | References: | 23 |
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